Partial regularity of minimizers of p(x)-growth functionals with p(x)>1. (June 2017)

• Record Type: Journal Article
• Authors: Nio, Erika; Usuba, Kunihiro
• Is Part Of: Nonlinear analysis. Volume 156(2017)
• Page Start: 197
• Page End: 214
• Publication Date: 2017-06
• Subjects: Variational integral -- Minimizer -- Non-standard growth -- Variable exponent -- Lower order term; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.01.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove partial regularity of minimizers u for functionals of the following type A ( u ) = ∫ Ω [ ( A i j α β ( x, u ) D α u i D β u j ) p ( x ) / 2 + g ( x, u, D u ) ] d x, assuming that A i j α β ( x, u ) and p ( x ) are sufficiently smooth and that p ( x ) > 1 . We prove that u ∈ C 0, α ( Ω 0 ) for some α ∈ ( 0, 1 ) and an open set Ω 0 ⊂ Ω with H m − γ 1 ( Ω − Ω 0 ) = 0, where H s denotes the s -dimensional Hausdorff measure and γ 1 = inf Ω p ( x ) .